Reconstruction theorem for monoid schemes

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Pirashvili, Ilia¹ 

[1] Univ Augsburg, Univ Str 14, D-86159 Augsburg, Germany

关键词: Commutative monoid;    Monoid scheme;    Topos;    Localisations of categories;    Topos points;   

DOI  :  10.1016/j.jpaa.2021.106782

来源: Elsevier

【 摘 要 】

We aim to reconstruct a monoid scheme X from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes X, we show that the localisations of the topos Q(c)(X) of quasi-coherent sheaves on X are in a one-to -one correspondence with open subsets of X, while the elements of X correspond to the topos points of Q(c)(X). This allows us to reconstruct X from Q(c)(X). (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free